Ratios and Proportions
Solving Proportions
Proportions can be
Solved when
Three of the
Four Parts of the
Proportion are known.
Solving
for an Unknown
When one Value
is Unknown, that
Value is assigned a
Letter.
Most commonly, that
Letter
is X.
A Proportion
with one Unknown.
3
:
4
::
X
:
8
Solving
for X
(1) Find the
Means and the
Extremes.
3
:
4
::
X
:
8
Means
3
:
4
::
X
:
8
Extremes
(2) Multiply the Means
and place the Product
to the Left of the
Equal Sign.
3
:
4
::
X
:
8
4
X
=
(3) Multiply the Extremes
and place that Product
to the Right of the
Equal Sign.
3
:
4
::
X
:
8
4
X
=
3 * 8
4
X
=
24
(4) Solve for
X by
Dividing the
Number opposite
the X by the
Number
beside the X.
X
=
24
÷
4
X
=
6
(4) Replace the
X in the original
Proportion.
3
:
4
::
X
:
8
3
:
4
::
6
:
8
More Examples of
Solving Proportions
3
:
10
::
6
:
X
10 * 6
=
3X
60
=
3X
60 ÷ 3
=
X
20
=
X
3
:
10
::
6
:
X
3
:
10
::
6
:
20
* * * * * * *
5
:
15
::
X
:
3
15X
=
5 * 3
15X
=
15
15 ÷ 15
=
X
1
=
X
5
:
15
::
X
:
3
5
:
15
::
1
:
3
* * * * * * *
2
:
7
::
8
:
X
7 * 8
=
2X
56
=
2X
56 ÷ 2
=
X
28
=
X
2
:
7
::
8
:
X
2
:
7
::
8
:
28
* * * * * * *